Finite Group Databasebeta

← #29600687

Subgroups — #29600687

Order 15616.

294 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458952C211yesmaximal, characteristic, complemented
2#21448134C211yesmaximal, characteristic, complemented
3#21448131C211yesmaximal, characteristic, complemented
4#21447923C211yesmaximal, characteristic, complemented
5#21444005C211yesmaximal, characteristic, complemented
6#21443958C211yesmaximal, characteristic, complemented
7C61×#1418C211yesmaximal, characteristic, complemented
8#135×D61—21no—
9#16840204—21no—
10#16840201—21no—
11#16840199—21no—
12#16840196—21no—
13#16840194C2211yescharacteristic
14#16840192—21no—
15C2×D976C2211yescharacteristic, complemented
16C2×#14519716C2211yescharacteristic
17#16839999—21no—
18#16839601—21no—
19#16839599—21no—
20D1952—21no—
21#16839597—21no—
22#16839596C2211yescharacteristic, complemented
23#16839562—21no—
24C61×#508C2211yescharacteristic
25C61×M64C2211yescharacteristic, complemented
26C61×#367C2211yescharacteristic, complemented
27#41×D61—41no—
28#14519800—21no—
29#14519799—21no—
30#14519798—41no—
31#14519797—41no—
32#14519796—21no—
33Q16×D61—21no—
34SD16×D61—41no—
35C2×D488—21no—
36D8×D61—21no—
37C2×C8×D61D411yescharacteristic
38#14519752—41no—
39Dic488D411yescharacteristic, complemented
40#14519723—21no—
41#14519722—21no—
42#14519721—21no—
43#14519720—21no—
44D976—21no—
45D976—21no—
46D976D411yescharacteristic, complemented
47#14519718—21no—
48#14519716—21no—
49#14519716—21no—
50C2×#11758185D411yescharacteristic
51#14519697—41no—
52#14519683—21no—
53#135×C61—21no—
54Q32×C61D411yescharacteristic, complemented
55SD32×C61—21no—
56D16×C61D411yescharacteristic, complemented
57C2×C16×C61C2311yescharacteristic
58#107×C61—21no—
59C32×C61—21no—
60#41×C61—41no—
61#11758226—41no—
62Q8×D61—41no—
63#11758224—41no—
64#11758224—81no—
65D4×D61—41no—
66D4×D61—81no—
67#11758222—41no—
68#11758222—81no—
69C2×D244—41no—
70C2×D244—81no—
71C2×C4×D61—81no—
72C2×C4×D61D811yescharacteristic
73Q16×C61—21no—
74SD16×C61—41no—
75D8×C61—21no—
76C2×C8×C61C2×D411yescharacteristic
77C4⋊C4×C61—41no—
78#11758202—41no—
79#11758201—41no—
80#11758200—41no—
81#11758199—41no—
82#11758198—81no—
83C2×#92418D811yescharacteristic
84Dic244—21no—
85D488—21no—
86D488—41no—
87D488—41no—
88#11758190—41no—
89C8×D61—21no—
90C8×D61—21no—
91C16×C61C2×D411yescharacteristic
92C16×C61C2×D411yescharacteristic
93#11758185—21no—
94C22×D61—81no—
95C22×D61—81no—
96C22×D61D1611yescharacteristic
97Q8×C61—41no—
98D4×C61—41no—
99D4×C61—81no—
100C2×C4×C61—81no—
101C2×C4×C61—81no—
102C2×C4×C61C2×D811yescharacteristic
103C22⋊D61—81no—
104C22⋊D61—81no—
105C22⋊D61—81no—
106C2×Dic61—81no—
107C2×Dic61D1611yescharacteristic
108D244—41no—
109D244—81no—
110D244—81no—
111D244—81no—
112D244—162no—
113C4×D61—21no—
114C4×D61—21no—
115C4×D61—81no—
116C4×D61—81no—
117C4×D61—81no—
118Dic122—41no—
119Dic122—81no—
120C8×C61#12011yescharacteristic
121C8×C61AGL(1,ℤ/8)11yescharacteristic
122#92418—21no—
123#13667—611nomaximal, Sylow
124C22×C61—81no—
125C22×C61C2×D1611yescharacteristic
126C2×D61—21no—
127C2×D61—41no—
128C2×D61—81no—
129C2×D61—162no—
130C2×D61—161no—
131C2×D61—161no—
132C2×D61—161no—
133C4×C61—81no—
134C4×C61—161no—
135C4×C61#44711yescharacteristic
136C4×C61#50911yescharacteristic
137Dic61—21no—
138Dic61—81no—
139#3414—611no—
140#2263—611no—
141#2263—611no—
142#2218—611no—
143#1418—611no—
144#1418D6111yescharacteristic, complemented
145#1400—611no—
146C2×C61—21no—
147C2×C61—161no—
148C2×C61#218411yescharacteristic
149D61—41no—
150D61—161no—
151D61—321no—
152C2×#135—1221no—
153#510—1221no—
154#510—1221no—
155#509—1221no—
156#509—1221no—
157#508—611no—
158#508—1221no—
159#508C2×D6111yescharacteristic
160C2×D16—611no—
161C2×M32—611no—
162#466—1221no—
163SD64—1221no—
164SD64—1221no—
165D32—1221no—
166D32—1221no—
167M64—611no—
168M64C2×D6111yescharacteristic, complemented
169#367C2×D6111yescharacteristic, complemented
170#357—1221no—
171C61#1366711yescharacteristic, complemented, Sylow
172C2×#41—2441no—
173#135—21no—
174#135—1221no—
175#135—1221no—
176#135—1221no—
177#135—2441no—
178#135—2441no—
179C2×Q16—1221no—
180C2×SD16—2441no—
181C2×D8—1221no—
182C2×D8—1221no—
183C22×C8—611no—
184#121—2441no—
185Q32—611no—
186Q32—1221no—
187Q32D24411yescharacteristic, complemented
188SD32—21no—
189SD32—1221no—
190SD32—1221no—
191SD32—1221no—
192D16—611no—
193D16—1221no—
194D16—1221no—
195D16—1221no—
196D16D24411yescharacteristic, complemented
197M32—1221no—
198M32—1221no—
199C2×C16—611no—
200C2×C16C22×D6111yescharacteristic
201#107—21no—
202#102—2441no—
203C32—21no—
204C32—1221no—
205#41—41no—
206#41—4881no—
207#41—4881no—
208#41—2441no—
209#41—2441no—
210#41—2441no—
211C2×Q8—2441no—
212C2×D4—4881no—
213C2×D4—4881no—
214C2×D4—2441no—
215C2×D4—2441no—
216C22×C4—611no—
217C22×C4—4881no—
218Q16—21no—
219Q16—1221no—
220Q16—2441no—
221SD16—41no—
222SD16—2441no—
223SD16—2441no—
224SD16—2441no—
225D8—21no—
226D8—1221no—
227D8—2441no—
228D8—2441no—
229D8—2441no—
230C2×C8—611no—
231C2×C8—1221no—
232C2×C8—1221no—
233C2×C8D4×D6111yescharacteristic
234C4⋊C4—41no—
235C22⋊C4—4881no—
236C16—1221no—
237C16C2×D24411yescharacteristic
238C16D4×D6111yescharacteristic
239C23—611no—
240C23—4881no—
241C23—4881no—
242Q8—41no—
243Q8—4881no—
244Q8—2441no—
245D4—41no—
246D4—81no—
247D4—9762no—
248D4—4881no—
249D4—4881no—
250D4—4881no—
251D4—4881no—
252D4—4881no—
253D4—4881no—
254D4—2441no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—611no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—4881no—
261C2×C4—4881no—
262C2×C4—4881no—
263C2×C4—4881no—
264C2×C4D8×D6111yescharacteristic
265C8—1221no—
266C8#1451974711yescharacteristic
267C8#1451980411yescharacteristic
268C22—81no—
269C22—1221no—
270C22—9761no—
271C22—9761no—
272C22—9762no—
273C22—9761no—
274C22—4881no—
275C22—2441no—
276C22D16×D6111yescharacteristic
277C4—81no—
278C4—161no—
279C4—1221no—
280C4—4881no—
281C4#1683989711yescharacteristic
282C4#1684019911yescharacteristic
283C2—21no—
284C2—161no—
285C2—19521no—
286C2—9761no—
287C2—2441no—
288C2#2144773211yescharacteristic
subgroupG/H
centerC2#21447732
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1418C2
socleC2×C61#2184
hypercenter#1418D61
hypocenterC61#13667
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1418

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21458952C2semidirect
2. #21448134C2semidirect
3. #21448131C2semidirect
4. #21447923C2semidirect
5. #21444005C2semidirect
6. #21443958C2semidirect
7. C61×#1418C2semidirect
15. C2×D976C22semidirect
22. #16839596C22semidirect
25. C61×M64C22semidirect
26. C61×#367C22semidirect
39. Dic488D4semidirect
46. D976D4semidirect
54. Q32×C61D4semidirect
56. D16×C61D4semidirect
144. #1418D61semidirect
168. M64C2×D61semidirect
169. #367C2×D61semidirect
171. C61#13667semidirect
187. Q32D244semidirect
196. D16D244semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214589522
#214481342
#214481312
#214479232
#214440052
#214439582
C61×#14182
#1366761